F-curves ignore custom "transform orientation"
Because the fcurves (like PGmath has indicated) are in global-space, you might be able to get done what you want with a small work-around:

For each piece of your sphere, add an empty at the center of the sphere and parent that one piece to it. Then rotate each empty such that the sphere-piece is directly below the empty. Apply the rotation to the empty, then manually rotate the empty back so the sphere-piece is back to its original location/orientation.

Any subsequent changes to the z-rotation of the sphere-piece should cause the rotation you are looking for. If you need an example .blend, I might be able to put one together and post it later today.